LCM for 20, 24 and 25

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

What's the Least Common Multiple (LCM) of 20, 24 and 25?

Answer

LCM of 20, 24 and 25 is
600

(Six hundred)

600 is the smallest positive integer that 20, 24 and 25 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 20, 24 and 25 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

All Prime Factors of 25: 5 × 5 (exponent form: 52)

Prime factor202425Highest power
22223—23
3—3—3
55—5252

LCM = 23 × 3 × 52 = 600

Checking the LCM of 20, 24 and 25 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(20, 24) = (20 × 24) ÷ 4 = 480 ÷ 4 = 120

LCM(120, 25) = (120 × 25) ÷ 5 = 3,000 ÷ 5 = 600

LCM(20, 24, 25) = 600

The pairs may be taken in any order — 24 and 25 first, then 20 — and the answer is the same 600. That is exactly why the two routes on this page agree.

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See Also

About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 20, 24 and 25? (The answer is: 600). Enter the first number (e.g. '20'), the second (e.g. '24') and the third (e.g. '25'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
102024120
1120241,320
122024120
1320241,560
142024840
152024120
162024240
1720242,040
182024360
1920242,280
202024120
202124840
2022241,320
2023242,760
202424120
202425600
2024261,560
2024271,080
202428840
2024293,480
202430120
2024313,720
202432480
2024331,320
2024342,040
202435840
202436360
2024374,440
2024382,280
2024391,560

FAQ

What's the Least Common Multiple (LCM) of 20, 24 and 25?

LCM of 20, 24 and 25 is 600

How to find the LCM of 20, 24 and 25 by prime factorization?

Take every prime that appears in 20, 24 and 25 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² = 600.

Can you get the LCM of 20, 24 and 25 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 20 and 24 is 120, and the LCM of 120 and 25 is 600 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 600 divisible by 20, 24 and 25?

Yes, and by definition it is the smallest positive integer that is: 600 ÷ 20, 600 ÷ 24 and 600 ÷ 25 all come out whole. Any other common multiple of 20, 24 and 25 is a multiple of 600.

See Also